Hey...so im having trouble with this question.....cant seem to figure it out:
The radar screen of an airport control tower shows that two planes are at the same altitude. According to the range finder, one plane is 100 km away, in the direction N60°E. The other is 160 km away, at a direction of S50°E. How far apart are the planes?
can i have some help?
Draw a diagram, and review the law of cosines. The distance can be found via
d^2 = 100^2 + 160^2 - 2*100*160 cos70°
d = 157 km
Thanks for your help!
d = 100[60+180]+160[130o]
d = (100*sin240+160*sin130)+(100*cos240+160*cos130)i
d = 36-153i.
d = sqrt(36^2+153^2) = 157 km.
Of course, I can help you with that question!
To find the distance between the two planes, we can use the Law of Cosines. The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.
First, let's draw a diagram to visualize the problem. We have two planes, and we know their distances from the control tower and the directions they are in.
From the information given, we know that Plane A is 100 km away in the direction N60°E and Plane B is 160 km away in the direction S50°E.
Now, let's break down the given information into the components we need.
For Plane A:
Distance: 100 km
Direction: N60°E
Since the direction is given in an angle relative to North, we can split it into its north and east components.
North component = distance * cos(angle) = 100 km * cos(60°) = 100 km * 0.5 = 50 km
East component = distance * sin(angle) = 100 km * sin(60°) = 100 km * 0.866 = 86.6 km
For Plane B:
Distance: 160 km
Direction: S50°E
Similarly, we can split the direction of Plane B.
North component = distance * cos(angle) = 160 km * cos(50°) = 160 km * 0.6428 = 102.85 km
East component = distance * sin(angle) = 160 km * sin(50°) = 160 km * 0.766 = 122.56 km
Now, we have the components of both planes in terms of north and east directions. The distance between the planes can be found using the Pythagorean Theorem, as they form a right-angled triangle.
Distance between the planes = square root of [(North component of Plane A - North component of Plane B)^2 + (East component of Plane A - East component of Plane B)^2]
Plugging in the values, we get:
Distance between the planes = square root of [(50 km - 102.85 km)^2 + (86.6 km - 122.56 km)^2]
After calculating this expression, you'll find the distance between the planes.